Daniel and Kelly’s Extraordinary Universe - Do things get more massive the faster they move?

Episode Date: July 11, 2023

Daniel and Jorge talk about what happens when you start to move fast, and whether it makes sense to think about your mass growing.See omnystudio.com/listener for privacy information.

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Maximize your edge by shopping at Lenovo.com during their back-to-school sale. That's Lenovo.com. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, everything changed. There's been a bombing at the TWA terminal.

Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, terrorism. Listen to the new season of Law and Order Criminal Justice System On the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious. Wait a minute, Sam. Maybe her boyfriend's just looking for extra credit. Well, Dakota, luckily, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend's been hanging out with his young professor a lot.

He doesn't think it's a problem, but I don't trust her. Now he's insisting we get to know each other, but I just want or gone. Hold up. Isn't that against school policy? That seems inappropriate. Maybe find out how it ends by listening to the OK Storytime podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. And here's Heather with the weather. Well, it's beautiful out there, sunny and 75, almost a little chilly in the shade. Now, let's get a read on the inside of your car. It is hot. You've only been parked a short time, and it's already 99.

degrees in there. Let's not leave children in the back seat while running errands. It only takes a few minutes for their body temperatures to rise, and that could be fatal. Cars get hot, fast, and can be deadly. Never leave a child in a car. A message from NHTSA and the ad council. Hey Daniel, has particle physics done anything useful lately? You mean other than revealing the fundamental needs? nature of reality. Have you done that? I mean, it's a project. I mean, that's all nice and cool, but it doesn't really help me, you know, with the dishes or, you know, with my diet. I guess we did also invent the World Wide Web. That's pretty helpful. You mean web surfing? I would say that's

not the most helpful thing in my life. But that was a long time ago. Anyways, what have you done for us recently? Yeah, maybe we should be coming up with like a fundamental physics diet plan. It's just coffee and donuts all the time. Existential angst about the nature of the universe. I guess the problem with physics is that it says that the faster you go, the more mass if you get, right? That's kind of an anti-diet. I guess I was thinking, you know, black holes, something, something, something, liposuction, black holes. I don't know.

I didn't really have it worked out. Quantum cosmetic surgery. Whoa. Orange County is definitely the place for that. And you can get a tan to the color beige. Hi, I'm Horhammy, cartoonist, and the creator of PhD Comics. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I was shocked when a pediatrician offered my one-year-old plastic surgery. Wait, what? They do that on one-year-old?

In Orange County, you're never too young for plastic surgery. Oh, boy. I get to the offer like a subscription service, like a membership or something. It's a long-term relationship. No, our son had like a vein on his eyelid, and the doctor was like, do you want me to remove that? We were like, no, please. Wait, the eyelid or the vein? You're like, I think my son needs it to his eyelid.

Exactly. We were like, I'm pretty sure that's going to be fine. and Newsflash is fine. Were you like, I'm a real doctor. I don't think he needs any surgery. I'm not a real doctor, but I'm pretty sure he didn't need any surgery. Like, I'm not a real doctor. I just play one in the lab.

But anyways, welcome to our podcast, Daniel and Jorge, explain the universe, a production of IHeartRadio. In which we try to show you the nature of the universe in all of its unvarnished glory. We don't want to edit out the ugly bits and smooth over the bumps and wrinkles. We want to show you the universe the way. it actually is, even when it conflicts with our intuition and runs the ground for our preconceived

ideas for how things move and flow and dance in the universe. That's right. That's because we love the universe just the way it is. We love the OG universe, the original organic version of the universe. Untreated, unvarnished, and pretty mysterious. That's right. We prefer the granola crunchy Berkeley version with all of its hair and all the original places, even on all of its black holes.

Whoa, whoa, whoa, let's not go too far there. I mean, I'm a big fan of socks and sandals, but, you know, there's a time and a place. I'm all for accepting people and universes just the way they are. But it is a wonderful and beautiful universe that doesn't need any cosmic surgery because when we look at it, we're just stricken with awe and amazement at how wonderfully complex and intriguing it all is. And one of my favorite things about the universe is that it's surprising. It's not like we look out into the universe and we're like, oh, yeah, that's pretty much how I expected.

Or, oh, yeah, there's nothing new out there to discover. Every time we dig deep into something, every time we scratch under the surface, we find out, wow, the universe is quite different from the way that we imagined it, which is wonderful because it's an opportunity to learn to discover the truth instead of just coasting on our intuition. Yeah, the universe is very different out there in space, beyond our galaxy, beyond our cluster of galaxies. And it's also very different at the molecular and atomic and particle scales. things are actually very different than our everyday experience. And we're tempted when we discover these new weird wrinkles in the universe to explain them in terms of things that we know, things we understand. It's a very natural way to try to understand the universe to describe it in terms of the

language that you already have. Sometimes though that gets awkward. It's hard to understand how quantum particles dance around if you're thinking about them as little dots of stuff. And that's because they're not really little dots of stuff. And it's hard to think about velocity and energy and mass. as things approach the speed of life because the definitions of those things have to change. And the way things move and bounce against each other and transfer energy and momentum is really

very different at high speeds than it is down here in the slow motion life on Earth. Yeah, things are very weird and awkward. In general, when you talk to physicists, I feel, not just when you learn what they have to say. All right, this is not a therapy podcast. We're talking about the nature of the universe here. That's right, that's right. And the universe is not awkward or weird. It's just the way it is.

And I guess it's us that are weird and awkward, right? because we have this picture of how the world works, but that may not be how the universe actually works. Yeah, and in physics, our project is to build a mathematical description of how things work in the universe, something that lets us make predictions and gives us a peek at the machinery behind the curtains that's deciding, like, what happens when two balls bounce against each other.

But that doesn't always translate in an easy or simple way to English, the language that most humans speak. So when physicists are trying to explain how things work when the universe gets weird, They use the terms that we're familiar with, mass and energy, momentum, et cetera, and try to translate the weirdness in those terms. And so you hear a lot of explanations for what happens when things get fast. Some of those explanations are bang on and some of them are a little bit misleading.

Yeah, because I guess one of the biggest mind-bending moments and odd as and strangest moments in the history of science was when we found out that the universe is kind of difference once you start moving really fast. Exactly. We've had Newtonian and Galilean mechanics for centuries, things that did a very good job of explaining what happens when two balls bounce against each other and how momentum is transferred and how things look when you're going fast. If you're driving in a car 30 miles an hour and you throw a ball at 30 miles an hour, then, you know, that ball should be

moving at 60 miles an hour relative to the ground. All that stuff made sense for a long time until we started looking at things that were moving really, really fast. We discovered there's a speed limit to the universe and that really changed everything we thought about the nature of space and time and velocity and gives rise to all sorts of weird stuff that's very tricky to unpack. Yeah, it gets super tricky. Well, first of all, the idea that we have a speed limit in the universe is kind of wild. Like, you know, you sort of grew up thinking that the sky's the limit. The more that you push something, the faster you go.

But at some point, the universe says, I think that's fast enough. It doesn't let you go faster than a certain speed. Yeah, it's a really bizarre feature of our universe, one that we've discovered experimentally. The Michelson-Morley experiments prove that light travels the same. speed in every direction and effectively demonstrating that there is no absolute reference frame and that there is a maximum speed of information and transmission in the universe, which leads to all sorts of weird consequences, changes what we think about time and the nature of simultaneity. Things that happen at the same time for one person might happen in a different

order for somebody else. The whole nature of reality becomes different when there is a maximum speed limit to the universe. Yeah, and I think it kind of makes people wonder what would happen And if you try to go faster than the speed of light, does the universe police come and flack you down and stop you? Do you hit a wall or what? Are you considering trying to break some laws to the universe? Are you asking for physics legal advice? Well, I'm trying to toe the line.

You know, I'm trying to max out my life here. I need to know how far I can go. I just don't want to be held responsible if you get thrown in physics jail. I'm going to need a physics lawyer. I wonder if people who are lawyers are always on the look at for like, is this person asking me legal advice? Am I going to get them in trouble if I say the wrong thing? I don't usually have to worry about that because most people are incapable of trying to break the laws of the universe.

I think most lawyers don't really care that much. But no, there is no physics police that are just going to pull you over. It's just that acceleration and momentum start working differently at high speeds. So you discover that you can pour energy into a particle, it just doesn't go much faster. So you could discover that as things approach to speed of light, you can keep pouring energy into something, a rock, a particle, a spaceship, whatever. It just doesn't go much faster. The same amount of energy doesn't get you, increases in velocity, the same rate. It's no longer linear.

It becomes asymptotic. So today on the podcast, we'll be tackling the question. Do things get more massive, the faster they move? This is kind of like the anti-dite, or at least it, I feel like it justifies maybe sitting down in your couch all the time. Because if I get up for my couch and I move, then I'm just going to gain more mass, right? Technically, that's true. Well, what we're going to learn on the podcast today is that it's a little bit more complicated than that. This is the kind of popular science thing you hear all the time and people write in and ask me about.

And I think it was widely taught in textbooks until about 30, 40 years ago. The feeling that everything gets weird as you approach the speed of light and that even your mass might change. Things might get like infinitely heavy as you approach the speed of light. It's an attractive concept for people, I think, because it gives you a sense of the strange. But as we'll talk about today on the podcast, it's a little bit more complicated. than that. And it's actually something of an outdated notion. Wait, wait. Are you saying it's a massive lie? You know, there's a lot of different ways you can try to translate the crisp mathematics

of relativity into English and into popular culture. This was one attempt early on that I don't think really works very well. I see. It was just heavily exaggerated. Well, as usually, we were wondering how many people had wondered about this question. I had asked this about themselves, about the universe, about what happens when you try to go faster and faster. And so Daniel went out They're into the internet to ask people, do you think things get more massive as you approach the speed of light? I am so grateful to everybody who answers these questions. They give me a sense for what people already know and they give listeners a sense for what

everybody else is thinking. If you would like to participate, please don't be shy. You're really very welcome to join the club. Just write to me to questions at danielandhorpe.com. So think about it for a second. Do you think you should stay in your couch if you don't want to gain any mess? Here's what people had to say. This question just blows my mind.

I'm just stumped. Do they get more massive? I guess maybe, I don't know how, but maybe something related to quantum mechanics, I don't know. As you approached the speed of light, I thought Einstein's equations told us that you would gain mass, but to an outside observer, I don't think you would actually look bigger.

I mean, at the speed of light time was slower. Maybe space gets contracted, so I'm kind of brainstorming here. Maybe if that is true, then you will have a higher density and in that sense will be more massive, not sure. I think they do get more massive, but because it gets harder to move things at that speed and not because they get more stuffy.

My understanding is mass and energy are interchangeable. So the more energy you have to pump into something to accelerate it, close. and closer to the speed of light is really no different than making it more massive to begin with. So I think, yes, it gets more massive as you approach the speed of light just because mass and energy are essentially the same thing. I think I remember hearing that they do get more massive as they approach the speed of light. Like it takes more energy to increase the speed and like, yeah, they just can't really get to the speed of light unless it's like, you know, massless. I guess so based on the question.

I'm not sure exactly why, but if it has something to do with like the kinetic energy of something affecting its mass, then I would guess so. I think the answer is yes. First, I was taught it that way. I've since heard that's an old school way of thinking about it. But definitely if we consider energy as being mass, you know, the way it works relativistically, you can concentrate energy as well as matter, and that is all mass energy. Then as you add velocity, you're adding energy and you become more massive. All right.

A lot of great answers here. I feel like some people were blown away and some people were like, oh, I've heard of this. The answer is yes or no. Yeah, I thought this was really interesting. There's a lot of different ideas here about what energy is and what mass is. Very few people have mentioned momentum even. But there's definitely this understanding that things change as you're the speed of light and that it's harder to go faster.

Yeah, somebody, one of the listeners said that it's kind of strange that your mass would change, right? And that goes to the heart of like what we mean by mass. I think a lot of people think of mass is like the amount of stuff they have. And so it's really weird for them to imagine them getting like more stuff as they approach the speed of light. And that's one reason why I really don't like this concept of relativistic mass. It gives people the impression that something physical is happening, which isn't.

Interesting. All right, well, let's dig into it. And I guess let's start with the basics, as you said. Let's start with the concept of mass. Now, I know mass is kind of a big mystery. We talked about it in our book. Like, what is mass? Anyways, you have a whole chapter about how we don't kind of know what mass is. But Daniel, maybe step us through it. What do we know about what mass is? I think in the context of relativity and motion, the most important thing to think about is inertia. Like the fact that it's not easy to change your velocity. You're flying through the universe. at some speed in order to change that speed you need a push right that's really what f equals m a is trying to say that to accelerate you need to have a force applied to you and that m in that equation and f equals ma is the mass it relates how much acceleration you get for how much force we've all heard for example that the earth's gravity on you is the same as your gravity on the earth right but we feel a much stronger force than the earth does because the earth has a huge mass So we feel a much stronger acceleration than the Earth does because the Earth has a huge mass.

And so its acceleration is tiny, even though the force is the same. So a really important concept in mass is inertia. That's really what mass is about when we're talking about motion. And that's connected to this idea of momentum, right? Another way to think about F equals MA is that F is actually a change in momentum. When you're flying through the universe at a certain velocity, you have a certain momentum. In order to change your momentum, you need to have a force applied. So mass is this concept that tells us basically how hard it is to change your momentum.

I feel like you're making us go down a rabbit hole a little bit because then it makes me wonder like what is momentum anyways? Yeah, and momentum is something we know is important in the universe. It's a quantity that's conserved. Like we look at in the universe, we watch stuff, we see things happen and we look for patterns. And a very important pattern are conservation laws, things that don't change. So two balls bounce against each other, for example. You calculate all the momentum beforehand and all the momentum. afterwards and you notice it's the same. It is conserved. We actually know that there's a deep

reason for why momentum is conserved. It's because space is the same everywhere. We did a whole fun podcast on Nuthers theorem, which tells you that because space is the same everywhere, momentum has to be conserved. This is deep link there. So momentum is an important physical quantity in the universe. It's something that's really powerful and really gives us insight into what's happening. Momentum is flowing through a system, right? But it's conserved in the universe. The universe, at least, thinks momentum is important. So maybe we should also. Well, how is it different from like energy? And is momentum the momentum of a particle or a baseball the same as its kinetic energy? How do the two connect? Yeah, great question. First of all, momentum has direction. You can have momentum in one direction or momentum

in another direction. It's a vector. It points. And for example, the earth has a constant magnitude of momentum, but the direction of its momentum is changing as it goes around the sun. It's like an arrow that tells you which way the Earth is headed, and that's constantly changing. So the length of that vector isn't changing, but the direction of it is. And that's why it takes acceleration to move around the sun, because you're changing the direction of that momentum vector.

So momentum is a direction, right? Energy doesn't have a direction. It's just a number, right? And also an energy includes something else. The energy of an object has two components. There's the internal energy, what we call it's inertial mass, and the energy of its motion, its kinetic energy.

So there's two separate. components there. So things could have energy when they're not moving, like an electron just sitting there has some mass, then that corresponds to some energy. And there's also energy of motion. Things can have only energy of motion, like a photon, is just motion energy, has no mass. Or they can have both, like an electron flying through the universe has mass and that's energy and also has kinetic energy. So energy has two components. There's the mass and it's a contribution from the momentum, which we also call kinetic energy. And so the universe conserves both things, right? Right? Like it somehow conserves momentum and it also conserves energy, but not necessarily in the same way, I think, right?

So there's a little asterisk there. In flat space, yes, energy is conserved in the global universe. As space expands, actually energy increases. So energy is not strictly conserved in the universe. There's a whole podcast episode we did about that if you want to dig into it. But let's just assume we're like living in flat space and we're bouncing balls and particles off each other. We wouldn't notice the expansion of the universe. So let's just say for the sake of this discussion, that yes, energy is conserved. And so you're right. Momentum is conserved and energy is conserved. And those are actually related. Those are four separate conservation laws because energy is one number and momentum is three numbers because we have three dimensions of space. And momentum is conserved separately in each of those dimensions. So we have four conservation laws, three from momentum and one from energy. And in particle physics, at least we group energy and momentum together

into something we call four momentum like the four dimensions of space time. And we say there's conservation of four momentum, which combines momentum and energy into one conservation law. So then mass is related to both things. Like mass makes your momentum go higher and it makes your energy go higher. Yeah, that's right. So mass is like your internal stored energy. Take a proton, for example. It has a bunch of mass. What does that mass come from? It comes from the internal energy of the proton. Like there's the mass of the quarks. They get their mass from the Higgs boson. Then there's the mass of the binding of those corks together. And that's where most of the mass of the proton comes from. So that proton has mass, and you're right, that's part of its energy.

And the proton could also have momentum. That's another part of its energy. So we think of the mass as the thing that makes it hard to push on something or easy to push on something if it has low mass. And then there's also energy stored in its motion. Okay. So then generally speaking, mass is just what makes things harder to move, right? Basically.

That's exactly right. That's the concept of inertial mass. Basically, it relate to the object's inertia, which tells you how hard is it to change its momentum. Right. And then there's a concept of gravitational mass, which is a different concept, but it's the same number. Yeah. And there's a bunch of really fascinating wrinkles here. Like in Newton's world, he had F equals M, which tells you about how hard it is to push something. And he also had this number M in his gravitational law, GMM over R square, which tells you the force between two objects. And in Newtonian physics, these two things are different numbers. They're

written in the same way, the same letter, M in F equals M, and M in GMM over R. are R squared, but in principle, they could have been totally different, right? It was a bit of a mystery in Newtonian physics, why these two numbers always seem to have the same value. Einstein unified these things in general relativity and told us that actually inertional gravitational masses have to be the same, because according to Einstein, there is no acceleration due to gravity, there is no force due to gravity. It's just inertial motion through curved space time.

That when you are having inertial motion, there's no forces on you, through space, time, that's what gravity looks like. So motion due to gravity is actually just inertial motion. You're just really in free fall. Right. So like, for example, the Earth orbiting around the sun, it's not like there's a force pulling the Earth towards the Sun or there's no centripetal force there. It's just that the space around the Sun for the Earth is sort of curved and it's shaped like a circle, basically, right? Yeah, that's right. If space were flat, everything would just move in what looks to us like straight lines. But when space is curved, things move. move differently. And it looks like there's a force there bending their paths, but really it's

just motion through curved space. Because we can't see that curvature, you can look through space and see the curvature of space the way you can like see the curvature of a road. It seems like a bit of a mystery why things are moving in curves. And of course, is that space is curved. So there's an apparent force there. Or more accurately, you mean like space time, right? Like maybe space is not curved, but space time is. It's definitely more coherent to think about relativity in terms of space time because the way like energy and momentum are linked, space and time are definitely linked. You can talk about the curvature of space as well and the curvature of time separately.

They make more sense when you think about them together. But yes, space itself can also be curved, but space time as well. All right. So then that's mass. It's how hard it is to push on something. And it's also sort of like the effects something has on space time around it. Yeah. And this is very intuitive.

If you're like playing billiards or you're shooting a basketball or you're rolling rocks downhills and it aligns with our sense that like things that have more stuff to them are harder to push and that all makes sense at low speeds things change a little bit as you get very high velocity and then you have a question for like what do you change you change momentum do you change mass do you change energy what's the most sensible way to think about these things yeah because as we mentioned there's the idea out there that the faster you go and as you approach the speed of light your mass starts to get bigger and bigger which is a problem for us who are trying to stay slim.

And so let's dig into that scenario and the problems with that scenario and what it all means about the loss of the universe. But first, let's take a quick break. Ah, come on. Why is this taking so long? This thing is ancient. Still using yesterday's tech, upgrade to the ThinkPad X1 Carbon, Ultra-Lite, Ultra-Powerful, and built for serious productivity with Intel core ultra-processors, blazing speed, and AI

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Apparently, the explosion actually impelled metal glass. The injured were being loaded into ambulances. Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, and it was here. to stay. Terrorism. Law and order criminal justice system is back. In season two, we're turning our focus to a threat that hides in plain sight. That's harder to predict and even harder to stop. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or

wherever you get your podcasts. My boyfriend's professor is way too friendly. and now I'm seriously suspicious. Wait a minute, Sam, maybe her boyfriend's just looking for extra credit. Well, Dakota, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend has been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone.

Now, hold up. Isn't that against school policy? That sounds totally inappropriate. Well, according to this person, this is her boyfriend's former professor and they're the same age. And it's even more likely that they're cheating. insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person to believe him because he now wants them both to meet. So, do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the

OK Storytime podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. I'm Dr. Scott Barry Kaufman, host of the Psychology Podcast. Here's a clip from an upcoming conversation about exploring human potential. I was going to schools to try to teach kids these skills and I get eye rolling from teachers or I get students who would be like it's easier to punch someone in the face. When you think about emotion regulation, like you're not going to choose an adaptive strategy which is more effortful to use unless you think there's a good outcome as a result of it if it's going to be beneficial to you because it's easy to say like go you go blank yourself right? It's easy. It's easy to just drink the extra beer. It's easy to ignore

to suppress seeing a colleague who's bothering you and just like walk the other way. Avoidance is easier, ignoring is easier, denial is easier, drinking is easier, yelling, screaming is easy. Complex problem solving, meditating, you know, takes effort. Listen to the psychology podcast on the IHeartRadio app, Apple Podcasts, or wherever you get your podcasts. topic here, and it's going by really fast, and it's about how really massive things go really fast. How things get massive as they go really fast. Yeah, things definitely do change as you approach the speed of light, and a lot of your intuition goes out the window.

You can just lean into the mathematics and say, well, there are new formulas, and I can just use them and calculate stuff. But we also want to have like an understanding of how the universe works. We want to develop a new intuition. So it's important that we make sense of what the words mean as things change. Okay, so let's talk about change, I guess. Now, before, when we just had Newtonian physics, things were kind of simple. Like, if you wanted to change the velocity of something, you had to apply a certain force.

And a certain force would always give you the same amount of velocity change, kind of. Like, no matter if you were standing still or if you're going fast, if you applied an F, you always got that change in velocity, the acceleration. Yeah, that's right. F used to equal MA in a very simple and straightforward way. or equivalently, we could say F is the change in momentum. Right. So that's Newtonian physics. But then we sort of learned a little bit more about relativity, which says that that's not quite true.

Yeah, because there is a maximum speed to the universe, if you pour energy into something to try to get it going faster, you don't always get the same amount of speed up, which means like it's harder to add velocity in the direction something is moving. You have a rocket chip and it's already going at 90% of the speed of light and you fire the engine. the same amount you did earlier, you're not going to get the same amount of speed up, even if you're applying the same force. Right, because I guess under Newtonian physics, you could technically go infinitely fast, right? Like if you just kept pushing on an object over a long, long period of time, we'd just keep going faster and faster and faster because F equals MA. And so if I apply a constant force to something,

the velocity is just going to keep increasing, increasing and increasing. And eventually it would go faster than the speed of light in a Newtonian universe. Yeah, that's exactly right. But we seem to have this speed limit that says you can go faster and faster. And so I guess my question is, what happened then? Did we have to adjust our math or does the math tell you why you can't go faster than the speed flight? We definitely had to adjust our math, right? Because those formulas are wrong.

As you say, they predict you could go infinitely fast. So what was wrong about those formulas? Well, it turns out our formula for momentum was wrong. We thought momentum was just like mass times velocity. And we thought that quantity was conserved in the universe. Turns out we were missing a term. There's another term in that equation. This thing we call the boost factor.

We write it as gamma in relativity. It's just a number. But if you're going at slow speeds, that number is basically one, so it doesn't change your equation. But as you approach the speed of light, that number grows to infinity. So what it means is momentum is different from what we thought it was. We talked about how momentum is this important quantity

in the universe that's conserved. That's true, but it's not m times v. There's a different expression for momentum, and that's the thing that's actually. that's actually conserved in the universe it turns out m times v times this gamma factor so momentum changes as you approach the speed of light and that's why it's harder to increase your velocity as you approach the speed of light because your momentum is changing it requires a larger force to change your momentum i guess this is where it gets kind of confusing because first of all like

you saying that as i go faster my momentum decreases but doesn't that depend on how How fast I'm going relative to who or what? Like, to me, I'm not going fast at all. If I'm going really fast, to me, it just looks like the universe is moving around me. So, first of all, as you go fast, your momentum still increases. That's always true. It's just not a linear increase. And you're absolutely right that all of these things depend on your frame, right?

Depends on who's watching. Somebody who's in a spaceship with you is going to see you at zero velocity. And somebody who's on Earth as you zip by is going to see you moving at very high speed. So you're absolutely right. There's no sense of talking about like, what is my velocity in an absolute way? It's always measured relative to some observer. So there's an important difference between things

that are invariant where everybody agrees in them no matter of their velocity and things that are conserved, things that don't change in a frame of reference. So momentum, for example, is conserved. For some observer, you always see momentum conserved. Like before collision, after collision, this is the same momentum.

But momentum is not invariant. Another observer moving at a different speed will see a different set of momentum, but they will also see momentum conserved. So momentum is conserved, meaning for a given observer, it doesn't ever disappear or appear, but it's not invariant, meaning different people will measure different amounts at different velocities. Okay, so then I think what you're saying is that momentum is not linear. It gets kind of wonky the faster you go. And the way it gets wonky is that it gets kind of ridiculously

big as you get closer to the speed of light, right? You said momentum equals mass time velocity times gamma and gamma is basically one when we're standing still but it gets to infinity as we get closer to the speed of light exactly and if you think about force not just as math times acceleration but as the change in momentum then if your momentum is really really big then it becomes hard to change your momentum you need to apply a really really big force to change your momentum and your momentum grows very very quickly near the speed of light as you say it approaches infinity as velocity approaches the speed of light so I guess but like get more concretely would mean like my couch, me sitting in my couch, my momentum would be

my mass times my velocity, which in this case, I guess it's zero, but it would just be my mass times my velocity. But if I was moving at 200,000 kilometers per second, then my momentum would be not just my mass times my velocity, but it'd be my mass times my velocity times a really big number, which is this adjustment factor that gets bigger, the closer you move to the speed of light. Exactly. This gamma factor is the thing that Newton missed in momentum. basically. And he missed it because for everything he measured and he saw, it was just one. So it didn't change any of his calculations. Any number multiplied by one is just itself. So you have like a hidden factor in your equations. That's always one. You can't discover it.

You can only discover it when it changes from one. And it only changes from one as you approach the speed of light. So I think kind of the message is that the universe is kind of like, okay, if you want to move something from your couch to your kitchen, that's fine. You can do that. It's going to cost you this much. But if you want to move it from, you know, your couch to almost to the speed of light or super duper fast, it's going to cost you that plus an extra like universe tax or something that says that, oh, that's going to cost you a lot, a lot. And somehow the idea is that it, that kind of lets the universe prevent you from going faster than the speed of light. Yeah. And this universe tax is basically zero if you're now moving very fast. Even if you're moving at like half the

speed of light, this gamma factor, this boost, this universe tax is like 15. percent. So even at half the speed of light, it's barely noticeable. As you get to like 90 percent of the speed of light, it's like 2.3. And if you get to like 99 percent of the speed of light, it's like 7, 99.9.9 percent of the speed of light, it's like 22. So it increases very, very quickly as things get fast. Well, I didn't know the universe was so progressive. Exactly. Momentum billionaires, the universe is coming for you. And so really that's fundamentally what's happening. We like to think about momentum because that's something the universe conserves. That's something that's important to the universe, energy and momentum. And that's really what's driving this experience that it's

harder to accelerate as you get towards the speed of light. And remember that momentum is directional, right? And so adding velocity in the direction you're already going takes actually different amounts of momentum than adding velocity like perpendicular to your motion. It gets very complicated. So I think you're saying that momentum is conserved in the universe, but there's sort of a premium on higher momentum momentum is like the bigger momentum as somehow cost you more exactly and that raises the question like well what do we do about mass we used to have this notion that mass told us how hard it is to push something and in the old sense of momentum it's just mass times velocity then it all made sense and then you get the equation f equals m a very natural linear

relationship between acceleration and force that all changes when we change the definition of momentum You no longer have F equals MA. And so you have to think about like, what do you do with mass? I think you're saying like, we have this tax that the universe puts on momentum. Now, do you take that tax and fold it into the definition of mass or is mass still mass? But then you have this extra tax, which is not mass. Exactly. And so the modern idea, the one that most physicists use is exactly that is say, let's just leave mass alone.

Mass is related to your internal stored energy. Let's define mass to be something everybody agrees on no matter what their volumin. velocity is. And let's just change the definition momentum. So mass stays as M, whatever it was before. And now momentum is M times V and we conclude the gamma factor there in momentum. The other idea, the one that leads to this confusion is this concept of relativistic mass and say, oh, let's redefine mass to be mass times gamma. Let's fold that gamma factor into the mass. And that lets us keep momentum as mass times velocity because we like that equation. And so there's sort of a choice to be made there. Like, do you redefine momentum or do you redefine mass?

Well, I say it kind of depends on whether you define mass as how hard you are to push when you're just sitting on your couch or how hard you are to push at any point or no matter how fast you're moving. It's definitely a choice, right? It's a definition and you can make one choice or the other and the equations all work. I think it's more coherent. It makes more sense if you call mass, as you say, how hard it is to push you when you're sitting on your couch. It's tempting to say, well, it makes more sense to use mass as how. how hard it is to push when you're moving fast as well. But as we can dig into in a moment,

that doesn't actually hang together. You can't have just a single number that tells you how hard it is to speed up because that actually depends a little bit on the direction of your speed up. So relativistic mass is a little bit complicated and problematic. It doesn't really do that job. It doesn't let you use F equals MA again by redefining M.

I see. So I think maybe for the people who had heard that the faster you go or the closer you get to the speed of light, the more massive you get. What they probably heard at that time was that you do get harder to push as you get closer to the speed of light, but that doesn't mean that your mask went up, which is that there's an adjustment to your momentum or there's a premium to how much momentum cost, which makes it harder for you to push you, but it doesn't change how hard you are

to get off the couch. Yeah, and physics has sort of changed its mind about this. Even Einstein for a while used this concept of relativistic bass, and it was taught in textbooks. So people who were told, like, your mass increases as you approach the speed of light, that's not wrong. It just depends on what you mean by mass. So it really is our choice of what do we mean by this word mass. It used to have a very crisp and clear definition that everybody agreed about at low speeds. At high speeds, it becomes a little bit trickier.

And you can use the word relativistic mass. It's not like it's wrong. It's just a choice for how to organize the ideas. And now we think it makes more sense to just describe mass as how hard it is to push you when you're sitting on your couch. and to leave momentum to absorb all the messiness. I guess you're saying, like, mass can just be how hard it is to push you out of your couch, but we can introduce maybe a concept called relativistic mass, where people did introduce a concept called relativistic mass,

which is how hard you are to push at all speeds, and that changes the faster you go. That does change the faster you go, though I would say the two choices are not equal. I would say there's some problems with relativistic mass. I mean, problem number one is that it's just a number, whereas momentum is three numbers. It's a direction. And so if you're going to talk about how hard it is to change your momentum,

then if you have a high speed in one direction, you basically have a different relativistic mass in each direction because it's harder to push you in the direction you're already going fast than it is to push you perpendicular to that direction. So then you would need like a transverse relativistic mass and a longitudinal relativistic mass. It gets messy very, very quickly. Well, I think what you're saying is that it's not that it gets

message is just that the word relativistic mass is a vector. Like you have to define which way you're pointing your relativistic mass, just like you have to define which way you're pointing your momentum. Well, we already have that concept of momentum, right? So we don't really need a vector of relativistic mass. And the formula for relativistic mass, it turns out, is actually just energy divided by the speed of light. So relativistic mass doesn't actually give you anything new that you don't already have for momentum and energy. So sort of unnecessary, Whereas invariant mass, your rest mass is actually something independent and interesting. It tells you like, what is the thing?

You know, photons and electrons and protons all have different rest masses. It tells you a little bit about like what the thing is, what it has to it, which I think is more closely connected to like our intuitive idea for what mass is. It tells you something about like what you're made of. And I guess for people who maybe missed it or are not super familiar with this idea of directionality, I think what you're saying is that if I'm going really fast from here to Andromeda, for example, in one particular direction and I'm going at half the speed of light, then my momentum in the direction from here to Andromeda is really high because I'm going really fast. And so it's really hard to accelerate me more in the direction of Andromeda. But maybe if you're going along with me and you try to push me in a direction that's perpendicular to the side of the direction from here to Andromeda, then you're not going to notice me being super massive or having this huge relativistic.

mass is just going to feel to you like I'm sitting on the couch. Like I'm sitting on the couch in one direction, but I'm going really fast in another direction. Yeah, that's approximately true because your motion towards endromeda does change your overall velocity and the limit is on the total velocity in any direction, not just in one direction. But for the most part, that's true. You know, what happens at those very high speeds is like if you push in one direction, you don't get accelerated in the direction you were pushing because the pushing has a different

impact based on your momentum, right? And so in some directions, you already have a lot of momentum and other directions you don't have as much momentum. And so the pushing changes your momentum differently in those different directions. So force and acceleration no longer line up. So F doesn't equal MA at very high velocities. Instead, you have to use F equals change in momentum.

That's the real formula. I feel like you're kind of saying like, just forget about mass. Like you sitting on the couch, nobody cares about that. Really, what we care about is how hard you're hard to push in any particular direction. Is that kind of what you're saying, right? Like you're saying like rest mass, that's just the thing. It doesn't really change.

Nobody cares. What's really happening at these high speeds is that we think are happening with your momentum. Yeah, I'm saying let's talk about what's really important. And at high speeds, it's momentum that's important. Mass is still important. It's very interesting and very important. And it tells you like what the thing is. In particle physics, we talk about rest mass all the time.

Like we measure a particle. We're like, oh, what was its mass? Okay, it must be an electron. Or look, we found a new particle at 125 GEV mass. that's got to be something new. We've never seen a particle with that mass before. So mass is still very, very important, but it tells you something different.

It tells you something about the character, the nature, the existence, the identity of the particle. And what we're talking about here is like motion near the speed of light. That's all about momentum. And so really, let's talk about momentum when we're talking about very high speed motion and let's talk about mass when we're talking about,

you know, what the thing is made out of. I think those are two separate concepts and it's best to disentangle them is the point. point. Not that nobody cares about rest mass. It's just it doesn't help us understand motion near the speed of light as much. No, yeah, I know what you mean. My spouse definitely cares if I sit in my couch all day. But I think what you're saying is, I mean, for listeners, I think what you're saying is that if you've heard the phrase like your mass gets bigger as you go closer to the speed of light,

then really what you should hear in your head or how you should correct the person saying it is that your relativistic mass gets bigger as you get closer to the speed of light. and also comma asterisk nobody or modern physicists don't really talk about relativistic mass or use that as a concept Exactly. A relativistic mass is really just another way to say energy. Like the relationship in the formulas between relativistic mass and energy, they have exactly the same value. One is just multiplied by the speed of light squared. So they change in exactly the same way. So relativeistic mass is just another way to say like how much energy does something have. It's a way to try to combine the rest mass and the kinetic energy together into one like overall coherent energy. And then to say, oh, well, that's all a new kind of mass. We'll just say the energy, the part of the energy, the particles kind of like it's mass of motion. And I'm just here to say like, okay, let's just leave mass to be mass of a rest particle. And to talk about motion, we'll leave that as kinetic energy. We have to invent a concept called mass of motion.

We already have energy of motion. We already have this concept described. In other words, relativistic mass doesn't really add anything. If you already have momentum and you have energy. So let's leave mass to do its job and tell us about like the nature of the object when it's sitting on its couch. All right. Well, I think we've made that kind of clear.

And so let's get a little bit deeper into why this. term is not quite applicable or useful or helpful or even accurate and what it means about this speed limit of the universe and why it exists. But first, let's take another quick break. Ah, come on. Why is this taking so long? This thing is ancient. Still using yesterday's tech, upgrade to the ThinkPad X1 Carbon, Ultra light, ultra powerful, and built for serious productivity with Intel core ultra processors, blazing speed, and AI power. performance. It keeps up with your business, not the other way around. Whoa, this thing

moves. Stop hitting snooze on new tech. Win the tech search at Lenovo.com. Lenovo, Lenovo. Unlock AI experiences with the ThinkPad X1 Carbon, powered by Intel Core Ultra processors so you can work, create, and boost productivity all on one device. December 29th,

1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal. Apparently, the explosion actually impelled metal glass. The injured were being loaded into ambulances. Just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged, and it was here to see.

day. Terrorism. Law and order criminal justice system is back. In season two, we're turning our focus to a threat that hides in plain sight that's harder to predict and even harder to stop. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly. And now I'm seriously suspicious. Well, wait a minute, Sam. Maybe her boyfriend's just looking for extra credit.

Well, Dakota, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend has been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now, he's insisting we get to know each other, but I just want her gone. Now, hold up. Isn't that against school policy? That sounds totally inappropriate. Well, according to this person, this is her boyfriend's former professor and they're the same age.

And it's even more likely that they're cheating. He insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person to believe him because he now wants them both to meet. So, do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the OK Storytime podcast on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast.

I'm Dr. Scott Barry Kaufman, host of the Psychology Podcast. Here's a clip from an upcoming conversation about exploring human potential. I was going to schools to try to teach kids these skills, And I get eye rolling from teachers or I get students who would be like, it's easier to punch someone in the face. When you think about emotion regulation, like, you're not going to choose an adapted strategy, which is more effortful to use unless you think there's a good outcome as a result of it, if it's going to be beneficial to you. Because it's easy to say like, go you go blank yourself, right? It's easy. It's easy to just drink the extra beer.

It's easy to ignore, to suppress, seeing a colleague who's bothering you and just like walk the other way. Avoidance is easier. Ignoring is easier. Denials is easier. Drinking is easier. Yelling, screaming is easy. Complex problem solving, meditating, you know, takes effort. Listen to the psychology podcast on the iHeartRadio app, Apple Podcasts, or wherever you get your podcasts. sitting on our couches, who doesn't enjoy that? And when we're sitting on our couch going at zero velocity relative to other people, we have a certain amount of mass and a certain resistance to movement, which Daniel, I think you're saying,

that's what we should call mass, not how hard you are to push when you're going really fast. Exactly. I think the question you should ask yourself is like, what are you trying to talk about when you talk about mass? And for me, I want to talk about like, what is the thing made out of? What does it have stored inside of it?

And that really doesn't change when you go to high velocity. A proton moving at high speed doesn't have more stuff to it, doesn't have more gluons inside of it contributing to its mass. It's the same proton. It's just moving faster. It has energy of motion, which definitely will affect how you accelerate it and how you push it and how it responds to those pushes. But it doesn't change what it is fundamentally. And to me, mass is answering that question of like, what is in this thing? I guess a question would be, does your gravitational mass also change as you go faster or close to the speed of light?

or do you still have the same gravity or is that not even relevant in relativity? I think that's another reason not to use relativistic mass. If you think about relativistic mass of things getting more massive as they approach to speed of light, this is like mass of motion, then you're tempted to think that things should have more gravity as they're moving faster. And then you might go down the rabbit hole and be like, well, if I take a proton and give it a lot of speed, why doesn't it turn into a black hole? If I throw a baseball fast enough, why doesn't it collapse into a black hole? if it's gaining more relativistic mass, shouldn't that give it also more gravitational mass and

collapse, right? We talked about this once on a podcast. It's a really interesting and fascinating question because on one hand, the curvature of space time, the thing that could actually create a black hole for you doesn't just depend on mass. It also does depend on energy, right? General relativity tells us that space bends in response to mass and energy. And so you might think like, oh, it doesn't matter if you choose relativistic mass or inertial mass. It just depends on the mass and the energy altogether. And that's true, but general relativity is a bit more complicated than that. You don't just like add up all the mass and energy in space and say that tells you the curvature.

It's a stress energy tensor. There's all these components and some add and some subtract. It's very complicated. And the bottom line is that kinetic energy does not contribute to the curvature of space. We know this because we know that black holes exist for every observer. It's not like if I'm holding a baseball, I don't see a black hole and somebody zipping by at high speed. sees it as a black hole. That's not possible. Something's a black hole, it's a black hole for everybody. And so only the rest mass can contribute to making something a black hole, which is

a long way of saying relativistic mass confuses you because it makes you think that you should be adding mass to this object, which might lead it to collapse to a black hole, but that definitely doesn't happen. I see. So then we just stick to mass as the how hard it is to move me on my couch. And when we talk about going close to the speed of light, then we just should just say that momentum gets harder to change as you go faster and faster. Exactly. And those calculations in general relativity of like folding in kinetic energy, those are a beast. And I don't even think people have actually been able to do those calculations.

When they have to do them, they use the trick and say, oh, well, if there's a black hole in any frame, there's a black hole in every frame. So let's do this calculation in the simplest frame where the thing is at rest, where it just depends on its mass. I think nobody knows how to do that calculation. It's so complicated. But it's just another way of saying when we think about gravity also, not just like the inertial nature of the thing, but also the gravitational nature of the thing, how much it bends space time, it makes the most sense to think about it. Maybe it's easier to think about if you don't call something relativistic mass. But then I guess my question would be, why does momentum get harder to change? The faster you go. Yeah. That doesn't help you with that question, right? That's a very fundamental question about the universe. You're just calling things differently. It's still the same question. Yeah. It's still the same question. Why does the universe conserve this quantity? Mass times velocity times gamma. The fascinating thing is that that's what it conserves. It doesn't conserve mass times velocity. Newtonian momentum is not conserved in the universe. It's only this Einsteinian momentum mass times this gamma factor. That's the thing that's actually conserved in the universe. And you can see this if you take a class in special relativity and you like think about collisions at very, very high energies and you try to use like normal Galilean velocity.

addition formulas and you see the momentum is no longer conserved. So the universe conserves this quantity mass times velocity times gamma. Why? Well, that actually comes out of the invariance of space, right? Space is the same everywhere in the universe. That tells you that this quantity, mass times velocity times gamma, is the thing that's conserved. Why is that? It's because of the invariance of space. Space seems to be the same everywhere and that's why momentum is conserved. That's a deep principle in physics, Nother's theorem. Well, I think you're, you're creating a causality there a little bit, right? Like, you don't know that one causes the other.

It's just that they just both happen to be true. Well, Nothor's theorem tells us that there is a causality. It says that for every symmetry in the universe, there is a conserved quantity. And so, for example, the fact that there's no preferred direction in space leads to conservation of angular momentum. Or maybe the conservation of angular momentum is when space, it's invariance. Philosophically, I feel like you're making a conclusion there. Yeah, I think that conclusion does.

come from Nother's theorem. I understand the point you're making, but this is not like an equal sign, right? It's not like A equals B and therefore you can't infer causality. If you follow the derivation of Nother's theorem, then it definitely goes in one direction. These conservation laws definitely flow from symmetries in the equations. If you have a symmetry in the laws of physics, then it gives you these conservation laws. And it's everywhere, like even in quantum mechanics, like local gauge symmetry of quantum electrododynamics is the reason we have charged conservation in the universe. So these things are pretty deep. And what it tells us in this case is that it's mass times velocity times this gamma factor. That's the thing the universe cares about. And even if you don't like

Nother's theorem and you don't believe in it or whatever, observationally, that's what we've measured. Empirically, we like, look, this is the thing the universe seems to care about. This quantity, not mass times velocity. So in some sense, that's the fundamental thing. That's the thing that the universe is telling us it cares about. Right. That's what I mean. It's like, that's the thing that we know is true. And whether it's caused by asymmetry or it, it approves. the theory or whether it enables a symmetry, that's sort of a philosophical question a little bit. Yeah, a little bit. I mean, we're theoretical. Experimentally, you're right. This is the thing we measure and we notice the universe cares about. Absolutely. I guess then the question is, what does that say

about the universe? That it cares about something? Doesn't just sit in the couch all day? I think it tells us a little bit about the history of human thought. You know, we've been like grappling with how to deal with these new discoveries that we've made and how to talk about them. One of my favorite quotes from Einstein relates to this. He says, quote, the only justification for our concepts and systems of concepts is that they serve to represent the complex of our experiences. Beyond that, they have no legitimacy. By which he means like, you know, what is mass? What is momentum? What is force? They only make sense if they're talking about things we experience. We put these labels on things we see and experience in the universe and we try to give them meaning. And there's actually

Einstein originally who created this concept of relativistic mass when he was playing around with these equations and he was like, hmm, maybe it's useful to have this concept of mass that depends on your velocity. Later on, he abandoned it. He realized, no, that's kind of messy. And then later he said, it is not good to introduce the concept of relativistic mass of a moving body for which no clear definition can be given. He realized it was a bit messy. But, you know, even geniuses like Einstein can't immediately disentangle these discoveries when he makes them. It takes a few years, few decades of thinking about how this really lines up with our experience in the universe. What's the most sensible way to organize it.

In the end, it's just us talking about how humans think about these things. The math is very, very clear. There's no ambiguity about it. It's really just like, what do you mean by this word? I think the basic idea is that it is true that the faster you move, the harder it is to move faster. And so we should think about that as just momentum getting more and more expensive. The closer you get to the speed of light and not use the word mass to think about

how hard things are to move at those speeds. Yep. the universe has a higher tax for momentum billionaires. It's a progressive universe. Bernie Sanders and AOC would be proud. Until they start their own space company. All right. Well, we hope you enjoyed that.

Thanks for joining us. See you next time. Thanks for listening. And remember that Daniel and Jorge Explain the Universe is a production of IHeart Radio. For more podcasts from IHeart Radio, visit the IHeart Radio app. Apple Podcasts or wherever you listen to your favorite shows. Ah, come on. Why is this taking so long? This thing is ancient.

Still using yesterday's tech, upgrade to the ThinkPad X-1 Carbon, ultra-light, ultra-powerful, and built for serious productivity with Intel Core Ultra processors, blazing speed, and AI-powered performance that keeps up with your business, not the other way around. Whoa, this thing moves. Stop hitting snooze on new tech.

Win the tech search at Lenovo.com. Lenovo, Lenovo. Unlock AI experiences with the ThinkPad X-1 carbon powered by Intel Core Ultra processors so you can work, create, and boost productivity all on one device. December 29th, 1975, LaGuardia Airport.

The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then everything changed. There's been a bombing at the TWA terminal, just a chaotic, chaotic scene. In its wake, a new kind of enemy emerged. Terrorism. Listen to the new season of Law and Order Criminal Justice System on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. My boyfriend's professor is way too friendly, and now I'm seriously suspicious. Wait a minute, Sam. Maybe her boyfriend's just looking for extra credit.

Well, Dakota, luckily, it's back to school week on the OK Storytime podcast, so we'll find out soon. This person writes, my boyfriend's been hanging out with his young professor a lot. He doesn't think it's a problem, but I don't trust her. Now he's insisting we get to know each other, but I just want her gone. Hold up. Isn't that against school policy? That seems inappropriate. Maybe. Find out how it ends by listening. to the okay storytime podcast and the iHeart radio app apple podcast or wherever you get your podcasts this is an iHeart podcast